The narrow-V ship wake in a radar image is typically a bright V-shaped or wedge-like return with an angle of a few degrees. It is often seen in images from satellite-borne Synthetic Aperture Radar (SAR), especially when the ship is traveling in a direction close to the SAR track and when the wind is light. Though explanation for the narrow-V wake exists already, it has been recognized from the time of Seasat that the model is deficient at microwave frequencies higher than L-band. The purpose of this paper is to describe a new model for the narrow-V wake based on the theory of unsteady moving sources. It overcomes the deficiency and implies that the narrow-V wake could be useful for ship classification purposes.